Algebra : abstract and concrete, stressing symmetry
著者
書誌事項
Algebra : abstract and concrete, stressing symmetry
Prentice Hall, Pearson Education, Inc, c2003
2nd ed.
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
For upper level undergraduate courses in Abstract Algebra.
This introduction to modern or abstract algebra addresses the conventional topics of groups, rings, and fields with symmetry as a unifying theme, while it introduces students to the active practice of mathematics. Its accessible presentation is designed to teach students to think things through for themselves and change their view of mathematics from a system of rules and procedures, to an arena of inquiry. The text provides plentiful exercises that give students the opportunity to participate in and investigate algebraic and geometric ideas which are interesting, important, and worth thinking about.
目次
I. BASICS.
1. Algebraic Themes.
2. Basic Theory of Groups.
3. Products of Groups.
4. Symmetries of Polyhedra.
5. Actions of Groups.
6. Rings.
7. Field Extensions-First Look.
II. TOPICS.
8. Field Extensions-Second Look.
9. Solvability.
10. Isometry Groups.
Appendix A: Almost Enough About Logic.
Appendix B: Almost Enough About Sets.
Appendix C: Induction.
Appendix D: Complex Numbers.
Appendix E: Review of Linear Algebra.
Appendix F: Models of Regular Polyhedra.
Appendix G: Suggestions for Further Study.
Index.
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